Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      In recent years, one of the most interesting developments in quantum mechanics has been the construction of new exactly solvable potentials connected with the appearance of families of exceptional orthogonal polynomials (EOP) in mathematical physics. In contrast with families of (Jacobi, Laguerre and Hermite) classical orthogonal polynomials, which start with a constant, the EOP families begin with some polynomial of degree greater than or equal to one, but still form complete, orthogonal sets with respect to some positive-definite measure. We show how they may appear in the bound-state wavefunctions of some rational extensions of well-known exactly solvable quantum potentials. Such rational extensions are most easily constructed in the framework of supersymmetric quantum mechanics (SUSYQM), where they give rise to a new class of translationally shape invariant potentials. We review the most recent results in this field, which use higher-order SUSYQM. We also comment on some recent re-examinations of the shape invariance condition, which are independent of the EOP construction problem.

      Related collections

      Author and article information

      Journal
      2011-11-28
      2012-09-25
      1111.6467
      10.1088/1742-6596/380/1/012016

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      ULB/229/CQ/11/5
      J. Phys.: Conf. Ser. 380 (2012) 012016, 13 pages
      21 pages, no figure; communication at the Symposium Symmetries in Science XV, July 31-August 5, 2011, Bregenz, Austria
      math-ph math.MP quant-ph

      Comments

      Comment on this article